$87$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $98$ less than $4$ times the number of away team fans. How many home team and away team fans attended the game?
Answer: Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 87}$ ${x = 4y-98}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${4y-98}$ for $x$ in the first equation. ${(4y-98)}{+ y = 87}$ Simplify and solve for $y$ $ 4y-98 + y = 87 $ $ 5y-98 = 87 $ $ 5y = 185 $ $ y = \dfrac{185}{5} $ ${y = 37}$ Now that you know ${y = 37}$ , plug it back into ${x = 4y-98}$ to find $x$ ${x = 4}{(37)}{ - 98}$ $x = 148 - 98$ ${x = 50}$ You can also plug ${y = 37}$ into ${x+y = 87}$ and get the same answer for $x$ ${x + }{(37)}{= 87}$ ${x = 50}$ There were $50$ home team fans and $37$ away team fans.